Question

When you weigh yourself, are you actually reading the support force acting on you, or are you really reading your weight?

Answer 1

You are weighing the force acted upon you. On earth, your weight is the pull of gravity on your mass. Your weight is not a constant. On individual planets or moons, however, the pull is the same when in the same place relative to the core. 

Answer 2

You're reading BOTH of those.  They are equal.  If they weren't equal,
then you would be accelerating up or down.

You're reading both your weight on Earth, and the Earth's weight on you.